# Time and Work - Aptitude Questions and Answers - RejinpaulPlacement

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50.
A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was: [Bank P.O. 1998]

Solution:   (A + B)'s 1 day's work = (1/45 + 1/40) = 17/360.

Work done by B in 23 days = [(1/40) * 23] = 23/40.
Remaining work = [1 - (23/40)] = 17/40

Now, 17/360 work was done by (A + B) in 1 day.
17/40 work was done by (A + B) in [1 * (360/17) * (17/40)] = 9 days.

A left after 9 days.
51.
A can do a piece of work in 14 days which B can do in 21 days. They begin together but 3 days before the completion of work, A leaves off. The total number of days to complete the work is: [R.R.B. 2002]

Solution:   B's 3 day's work = [(1/21) * 3] = 1/7.
Remaining work = [1 - (1/7)] = 6/7.

(A + B)'s 1 day's work = [1/14 + 1/21] = 5/42

Now, 5/42 work is done by A and B in 1 day.
6/7 work is done by A and B in[(42/3) * (6/7)] = 36/5 days.

Hence, total time taken = [3 + (36/5)] days = 10   1/5 days.
52.
A, B and C can complete a work separately in 24, 36 and 48 days respectively. They started together but C left after 4 days of start and A left 3 days before the completion of the work. In how many days will the work be completed?

Solution:   (A + B + C)'s 1 day's work = [1/24 + 1/36 + 1/48] = 13/144

Work done by (A + B + C) in 4 days = [(13/144) * 4] = 13/36

Work done by B in 3 days = [(1/36) * 3] = 1/12.
Remaining work= [1 - [(13/36) + (1/12)]] = 5/9

(A + B)'s 1 day's work = [1/24 + 1/36] = 5/72.

Now, 5/72 work is done by A and B in [(72/5) * (5/9)] = 8 days.

Hence, total time taken = (4 + 3 + 8) days = 15 days.
53.
A, B and C together earn Rs. 300 per day, while A and C together earn Rs. 188 and B and C together earn Rs. 152. The daily earning of C is:

Solution:   B's daily earning = Rs. (300 - 188) = Rs. 112.

A's daily earning = Rs. (300 - 152) = Rs.148.

C's daily earning = Rs. [300 - (112 + 148)] = Rs. 40.
54.
A, B and C are employed to do a piece of work for Rs. 529. A and B together are supposed to do 19/23 of the work and B and C together 8/23 of the work. What amount should A be paid ? [C.B.I. 1997]

Solution:   Work done by A = [1 - (8/23)] = 15/23.

A : (B + C) = 15/23 : 8/23 = 15 : 8

So, A's share = Rs. [15/23) * 529] = Rs. 345
55.
Kim can do a work in 3 days while David can do the same work in 2 days. Both of them finish the work together and get Rs. 150. What is the share of Kim? [S.S.C. 1999]

Solution:   Kim's wages : David's wages = Kim's 1 day's work : David's 1 day's work
= 1/3 : 1/2 = 2 : 3

Kim's share = Rs. [(2/5) * 150] = Rs. 60
56.
If A can do 1/4 of a work in 3 days and B can do 1/6 of the same work in 4 days, how much will A get if both work together and are paid Rs. 180 in all?